An Equivalent Circuit Model for 2D Embroidery Using Conductive Threads

2D embroidery techniques, such as fill stitch, enable the creation of conductive areas in e-textiles, but predicting their electrical resistance is difficult due to dense rows simultaneously lengthening current paths and creating numerous inter-thread contacts. We present a physics-based equivalent circuit model that links these competing effects by modeling each inter-thread junction with a through-thread resistor in parallel with a contact resistor. Our method estimates fill stitch resistance from key parameters including thread resistivity and radius, fabric thickness, and stitch density. Evaluations with embroideries using 33 combinations of stitch densities, embroidery sizes, and shapes show that experimental results closely match our model's predictions. Our work provides a quantitative foundation for understanding and systematically designing 2D embroidered smart textiles.